1. Loan Workouts: Putting it All Together

2. Loan Workouts So far we’ve looked at:  Probability of success and failure over the entire loan records P(S) = 0.464 P(F) = 0.536  Expected Value of Workout E(X) = (Full Loan) P(S) + (Default) P(F)

3. Loan Workouts We also looked at the conditional probabilities of success and failure based on Y, T, and C  P(S|Y)  P(F|Y)  P(S|T)  P(F|T)  P(S|C)  P(F|C)

4. Loan Workouts We also looked at the expected value of each of our borrowers characteristics:  E(Z Y )  E(Z T )  E(Z C ) Unfortunately, none of these pieces of info helps for making a decision for our particular borrower

5. Loan Workouts We would like to be able find out expected value and probabilities using all of our borrower’s characteristics In other words:  P(S|Y&T&C) AND P(F|Y&T&C)  E(Z)

6. Loan Workouts Unfortunately our loan records do NOT contain enough information to compute  P(S|Y&T&C) AND P(F|Y&T&C) Why?  The loan records are incomplete across the three banks that were merged  Customer #1 in the loan records has information with respect to education level only No Info on Years of Business Experience or Economic Times

7. Loan Workouts Bayes’ Theorem to rescue  Allow us to find:  If we know:

8. Loan Workouts How? But the numerator portion can be expressed as:

9. Loan Workouts How do we compute: One of the project assumptions is that Y, T, and C are all independent of each other event if we consider successes or failures

10. Loan Workouts Knowing this we can say: We know need to find

11. Loan Workouts Let’s look at one of these and figure out its probability. Computations will be similar for the other two Consider: This is asking for the probability a borrower has the same # of years experience as your borrower given the workout was successful

12. Loan Workouts Because BR Bank was the only bank to keep records on borrowers years of experience, we only have their records to rely on: But since we can assume each bank made out loans to similar populations of borrowers, our estimation is a good one

13. Loan Workouts To find

14. Loan Workouts So if reproduce the same calculation for the other conditional probabilities we now know: From this we can also do similar calculations for:

15. Loan Work Out Tree Diagram S F (Y  T  C) (Y  T  C) C (Y  T  C) (Y  T  C) C P(S)P(S) P(F)P(F) P(Y  T  C | S) P(Y  T  C | F) P(S  Y  T  C) = P(S). P(Y  T  C | S) = P(S). P(Y|S). P(T|S). P(C|S) P(F  Y  T  C) = P(F). P(Y  T  C | F) = P(F). P(Y|F). P(T|F). P(C|F)